epsproc.calc.density module

Density matrix routines

30/08/21 v3 Debugged and updated docstrings. 27/08/21 v2 Updated dim handling for renaming multi-index levels + working HV plotting routines. 26/08/21 v1 Initial implementation

Dev code:

epsproc.calc.density.densityCalc(da, denDims='LM', sumDims=None, keepDims=None, selDims=None, thres=None, squeeze=True, keepNaNs=False, compute=True)[source]

General density matrix from Xarray.

Compute density matrix as (outer product) da[denDims]*da[denDims].conj(), where dim specifies the dimension(s) to use. This is, essentially, the density matrix :math:row = |denDims\rangle \langle denDims|:math:

Parameters:
  • da (xarray) – Data array to check & restack
  • denDims (str, list, dict, optional, default = 'LM') – Dimensions to use as “state vector” from da. If a single dim (including stacked dims), which exists, this will be used directly. If multiple dims, will be restacked to a new dimension. Note that this can mix stacked and unstacked dims, and will restack if necessary.
  • sumDims (str, list, bool, optional, default = None) – Set specific dims to sum (“trace”) over. If sumDims = True all dims, apart from denDims and keepDims, will be summed over.
  • keepDims (str, list, optional, default = None) – Define dims to keep (won’t be summed over). Only used if sumDims = True.
  • selDims (str, list, optional, default = None) – Dimensions to subselect from.
  • thres (float, optional, default = None) – Threshold value. If set, used for both input and output datasets.
  • squeeze (bool, optional, default = True) – Squeeze out singleton dims if True.
  • keepNaNs (bool, optional, default = False) – Keep NaNs in result if false. Otherwise, set to zero. (Note this is currently implemented indirectly via xr.sum(skipna = ~keepNaNs).) Note: in some cases this may cause NaNs to propagate and give all-NaN results.
  • compute (bool, optional, default = True) – Compute density matrix as outer product? Otherwise just set from restacked Xarray.

Notes

selDims, thres and squeeze are passed to the standard matEleSelector() function.

Examples

# Calculate for standard matE dataset, restacked for [l,m,mu]. >>> daOut, daDot = densityCalc(matE, denDims = [‘LM’, ‘mu’], selDims = {‘Type’:’L’}, thres = 1e-1) # Calculate for standard matE, no restack and sum all other dims. >>> daOut, daDot = densityCalc(matE, denDims = ‘LM’, selDims = {‘Type’:’L’}, thres = 1e-1, sumDims = True) # Calculate for standard matE, no restack and sum all other dims, except Sym. >>> daOut, daDot = densityCalc(matE, denDims = ‘LM’, selDims = {‘Type’:’L’}, thres = 1e-1, sumDims = True, keepDims = ‘Sym’)

epsproc.calc.density.dimRestack(da, stackDims=[])[source]

General Xarray restacker including multi-indexes.

Check dims in da, and restack according to refDims if necessary

Parameters:
  • da (xarray) – Data array to check & restack
  • stackDims (str, list, dict, optional, default = []) – Dimensions to check in da, and restack along if not already stacked. Note that this can mix stacked and unstacked dims, and will restack if necessary
Returns:

  • daOut (Xarray) – Data array with restacked dim.
  • stackedDim (str) – Name of new stacked dim
  • rsMap (dict) – Dictionary mapping for new stacked dim
  • dimCheck (dict) – Full output from ep.util.misc.checkDims()

Examples

>>> # Assuming matE is a standard array of matrix elements
>>> daOut, stackedDim, rsMap, dimCheck = dimRestack(matE)  # OK, returns input + dim check results
>>> daOut, stackedDim, rsMap, dimCheck = dimRestack(matE, stackDims='LM')  # OK, returns original dims
>>> daOut, stackedDim, rsMap, dimCheck = dimRestack(matE, stackDims=['LM','mu'])  # OK, restacks dims

Notes

Passing new mappings as stackDims is currently not supported, e.g. dMap = {‘NewDim’:[d1,d2…]} will fail. For this case, just use the native da.stack(dMap).

See also

multiDimXrToPD()

epsproc.calc.density.matPlot(da, kdims=None, pTypes=['r', 'i', 'a'], negQs=True, thres=None, returnType='plot', verbose=1)[source]

General matrix (2D) plot + stacked dims plotter with HoloViews.

Parameters:
  • da (Xarray) – Input dataset for plotting. Assumed to contain a “matrix” (2D) to plot, with other dims stacked to HV plot widgets.
  • kdims (list, optional, default = None) – Key dims for plotting. If None, - will be taken from da.attrs[kdims] if it is set. - otherwise, uses da.dims[-2:]
  • pTypes (list, optional, default = ['r','i','a']) – List of plot types to set (via :py:func:`epsproc.plotTypeSelector`_ These will be available via the HV plot widgets.
  • negQs (NOT YET IMPLEMENTED) – Include -ve valued QNs in plot?
  • thres (NOT YET IMPLEMENTED) – optional, float, default = None Threshold for plot.
  • returnType (str, optional, default = 'plot') – If ‘plot’ return plot object only. Otherwise, returns plot + datasets = (hvmap, hvds, daPlotDS)
  • verbose (int, bool, optional, default = 1) – Print additional info if true.
Returns:

If ‘plot’; otherwise, returns plot + datasets = (hvmap, hvds, daPlotDS)
Return type:

Holoviews holomap object

TODO:

  • update & consolidate dim-handling routines from densityCalc() to provide easier plotting routines here (without manual restack etc. for other data types).